Notes on general SIC-POVMs

Rastegin, Alexey E.

doi:10.1088/0031-8949/89/8/085101

Cited by 49 publications

(35 citation statements)

References 63 publications

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“…Various applications of the above entropies and their quantum counterparts are discussed in the book [17]. Analyzing the case of detection inefficiencies, we will use the method of [30,31]. To the given value η ∈ [0; 1] and probability distribution {p n }, one assigns a "distorted" distribution:…”

Section: Preliminariesmentioning

confidence: 99%

On Uncertainty Relations and Entanglement Detection with Mutually Unbiased Measurements

Rastegin

2015

Open Syst. Inf. Dyn.

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We formulate some properties of a set of several mutually unbiased measurements. These properties are used for deriving entropic uncertainty relations. Applications of mutually unbiased measurements in entanglement detection are also revisited. First, we estimate from above the sum of the indices of coincidence for several mutually unbiased measurements. Further, we derive entropic uncertainty relations in terms of the Rényi and Tsallis entropies. Both the state-dependent and state-independent formulations are obtained. Using the two sets of local mutually unbiased measurements, a method of entanglement detection in bipartite finite-dimensional systems may be realized. A certain trade-off between a sensitivity of the scheme and its experimental complexity is discussed.

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Section: Preliminariesmentioning

confidence: 99%

On Uncertainty Relations and Entanglement Detection with Mutually Unbiased Measurements

Rastegin

2015

Open Syst. Inf. Dyn.

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“…Previous generalizations of projective t designs to the arbitrary-rank case were either limited to specific subsets, such as SICs or MUBs [14][15][16][17][18], or relaxed the operational property of indistinguishability from the uniform distribution given t copies [19]. In this work, we introduce the class of mixed t designs as the most general extension of projective t designs that preserves the operational property of indistinguishability from the uniform distribution up to t copies, while relaxing the mathematical assumption of pure elements.…”

Section: Introductionmentioning

confidence: 99%

Communication capacity of mixed quantumt-designs

2016

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We operationally introduce mixed quantum t designs as the most general arbitrary-rank extension of projective quantum t designs which preserves indistinguishability from the uniform distribution for t copies. First, we derive upper bounds on the classical communication capacity of any mixed t design measurement, for t ∈ [1, 5]. Second, we explicitly compute the classical communication capacity of several mixed t design measurements, including the depolarized version of: any qubit and qutrit symmetric, informationally complete (SIC) measurement and complete mutually unbiased bases (MUB), the qubit icosahedral measurement, the Hoggar SIC measurement, any anti-SIC (where each element is proportional to the projector on the subspace orthogonal to one of the elements of the original SIC), and the uniform distribution over pure effects.

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“…Let general SIC-POVM N = {N i } be characterized by the parameter a in the sense of (2.21). For the given pre-measurement state ρ, we have [62]…”

Section: Some Forms Of Uncertainty Relationsmentioning

confidence: 99%

“…For a usual SIC-POVM, when a = d −2 , the result (3.30) is reduced to (3.27). For α ∈ (0; 2] and arbitrary density matrix ρ on H, one gets [62] R α (N |ρ) ≥ ln d(d + 1)…”

Section: Some Forms Of Uncertainty Relationsmentioning

confidence: 99%

Rényi and Tsallis formulations of separability conditions in finite dimensions

Rastegin

2017

Quantum Inf Process

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Separability conditions for a bipartite quantum system of finite-dimensional subsystems are formulated in terms of Rényi and Tsallis entropies. Entropic uncertainty relations often lead to entanglement criteria. We propose new approach based on the convolution of discrete probability distributions. Measurements on a total system are constructed of local ones according to the convolution scheme. Separability conditions are derived on the base of uncertainty relations of the Maassen-Uffink type as well as majorization relations. On each of subsystems, we use a pair of sets of subnormalized vectors that form rank-one POVMs. We also obtain entropic separability conditions for local measurements with a special structure, such as mutually unbiased bases and symmetric informationally complete measurements. The relevance of the derived separability conditions is demonstrated with several examples.

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Notes on general SIC-POVMs

Cited by 49 publications

References 63 publications

On Uncertainty Relations and Entanglement Detection with Mutually Unbiased Measurements

On Uncertainty Relations and Entanglement Detection with Mutually Unbiased Measurements

Communication capacity of mixed quantumt-designs

Rényi and Tsallis formulations of separability conditions in finite dimensions

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